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Measurement of electrical conductivity under conditions of high anisotropy in graphite intercalation compounds
Materials Science and Engineering, 31 (1977) 255 - 259
255
@) Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
Measurement of Electrical Conductivity under Conditions of High Anisotropy in Graphite Intercalation Compounds*
C. ZELLER, G. M. T. FOLEY, E. R. F A L A R D E A U and F. L. VOGEL
Moore School of Electrical Engineering and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (U.S.A.)
SUMMARY
Recent measurements of r o o m temperature electrical conductivity in AsFs-graphite intercalation compounds have emphasized the need for a re-evaluation of conventional techniques when applied to quasi-two-dimensional materials. We have thoroughly investigated the validity of the classic 4-point bridge measurement under conditions of high anisotropy and find that for parameters appropriate to some intercalation compounds, such techniques are impractical and lead to serious errors in measured electrical conductivities. In attempting to resolve the difficulties inherent in making measurements of electrical conductivity in these materials we have considered the Montgomery d.c. technique and a novel r.f. method. Measurements on AsFsgraphite by the Montgomery technique appear to give qualitatively correct behavior for resistivity v e r s u s stage and confirm that the magnitude of the anisotropy is larger than that in any previously measured compound. The technique is, however, critically sensitive to crystal defects and this precludes a definitive measurement of a-axis conductivity in these compounds. The r.f. technique which we have developed is, by contrast, insensitive to the degree of anisotropy and is shown to be well suited to the measurement of basal plane conductivities in quasi-two
de mesure conventionnelles appliqu6es ~ des mat6riaux quasi bi
INTRODUCTION RESUME
Des mesures r6centes de conductivit6 6lectriques ~ temp6rature ambiante sur des compos6s d'insertion graphite-AsFs ont indiqu6 clairement la n~cessit6 de reviser les m6thodes *Research supported by NSF DMR75-04954 and MRL/DMR 76-00678.
Relatively little attention has been paid in the past to the significance of the electrical anisotropy as it relates to measurement o f the electrical conductivity in graphite intercalation compounds. Recent results of measurements of the basal plane room temperature electrical conductivity of some of the
256 TABLE 1 a-Axis and c-axis conductivities of HOPG and some graphite intercalation compounds Material
Measurement technique
Bridge method
HOPG Cz2HNO 3 C16AsF 5 C8Rb CsK
r.f. Method
Anisotropy a -=- o a / o c
oa
ac
oa
(~2 cm) -1
(~2 cm) -1
( ~ cm) -1
11.4 [1] 1.96 [3] 0.23 [7] -4.8 x 104 [9]
2.6 × 3.3 x 6.3x 9.1 × --
2.7 x 2.7 × 2.2× 1.0 × 9.5 x
104 105 105 10 5 104
[1] [3] [5] [8] [8]
strong acid-fluoride intercalation compounds of graphite suggest that the choice of measuring technique is crucial. Reference to Table 1, a compilation of a-axis and c-axis conductivities for graphite and several intercalation compounds, reveals a substantial discrepancy between a-axis values for AsFs-graphite from two different types of measurement [5, 6]. The a-axis conductivity from a four point d.c. bridge measurement is almost a factor of three smaller than that derived by an r.f. eddy-current technique. The source of the discrepancy is the very large anisotropy ratio, a (-oa/oc), for AsFsgraphite which exceeds 106 for stages lower than four [7]. This is almost three orders of magnitude larger than the anisotropy ratio for the parent, highly-oriented, pyrolytic graphite [2] (HOPG) and indicates that the compound is quasi-two-dimensional in its electrical properties. The values of Table 1 show that the disparity between bridge measurements and r.f. measurements increases with increasing anisotropy. For HOPG with a ~ 2 000 the agreement between the two methods is rather good, as it is for CaRb [7, 9], where the anisotropy (inferred from that for CsK) [8] is even smaller. However, the acceptor intercalation compounds, in general, show marked increases in ~ over that for HOPG. Moreover, the acceptor compounds have recently become of special interest as possible practical synthetic metals [ 11 ]. It appears to be appropriate therefore, to review the practical and theoretical considerations in making reliable measurements of their room temperature basal plane conductivities.
104 105 105 10 4
[2] [4] [6] [10]
2.3 x 103 [1] 1.4 x 105 [3] 2.7 × 106 [7] -21 [9]
i
-
v
1 c-axis
Fig. 1. Bridge sample configuration.
In that regard we examine three techniques, and results of their application to AsF5graphite. These are the conventional 4-point d.c. bridge technique, the Montgomery method [12] and the r.f. induction technique [13]. Of the three, only the latter is entirely satisfactory.
EXPERIMENTAL TECHNIQUES
(i) The 4-point, d.c. bridge m e t h o d Figure 1 illustrates a typical sample configuration for these measurements. The fundamental premise of the technique is that there exists uniform current density between the voltage contacts. Although this condition is easily met for isotropic samples, in general, the premise can only be satisfied for anisotropic materials for thin samples with current contacts far from the voltage contacts. The necessary sample geometries cannot be achieved with AsFs--graphite where aspect ratios l/t ~- 104 are called for. The problem lies in the distribution of current at a current contact where current is typically injected by means of a gold wire wrapped around the contact and epoxied with a conducting gold cement. The real experi-
257 i
A
Rs
R%
IRWi
Re
RGc
R% ",ANVW,--
Rw i
RB
RGc
RG o
Rw
Re
RGc R% i i i i I
Re
~
R%
Fig. 2. Equivalent circuit for a bridge sample at a current contact.
mental situation is complicated, varies from one experiment to the next, and cannot therefore be modelled exactly. Nevertheless, simple models serve to illustrate the problems involved and enable reasonable conclusions to be drawn with respect to feasibility of 4-point bridge measurements. Figure 2 is a representation of an equivalent circuit for a bridge sample in the region of a current contact. Rw, Rs and RB represent the incremental wire resistance, surface contact resistance and the bulk contact resistance, respectively. RG, and RGc are resistances characterizing conduction along the basal plane and perpendicular to it, respectively. Relative weights of the resistors in the network for AsFs-graphite are: R w ~ RGa ~
Rec
and Rs << R B. The second inequality is motivated by the fact that a two
Further, it is consistent with results observed experimentally for AsFs-graphite. The nonuniform distribution of current is equivalent to an effective sample thickness smaller than the true thickness. This results in the observed underestimation of the basal plane conductivity. Model calculations of a "worst case" situation for AsFs-graphite, in which current is injected into and extracted from the top surface layer of the sample only, indicate resistivities two orders of magnitude higher than those observed experimentally in bridge measurements. While, in practice, therefore, we do not approach the "worst case" configuration, results of a detailed study of bridge measurements under conditions of very high anisotropy (~ >- 105) justify two general conclusions: (i) Uniform current injection at a current contact cannot be achieved in practice. (ii) Once injected non-uniformly, negligible current spreading takes place between the current contacts for samples of any reasonable length. Based on these conclusions, results of electrical conductivity measurements on highly anisotropic materials by the 4-point bridge technique must necessarily be considered unreliable. We therefore completely discount the low (2.2 × 105 (~ cm}-1} a-axis conductivity values for AsFs- graphite indicated in Table 1.
(ii) D.C. Montgomery technique This four-point technique permits determination of the conductivities along the principal directions in an anisotropic solid. For highly anisotropic materials the six-contact configuration of Fig. 3 is necessary. In measurements on AsFs-graphite we have used square plate samples 1 cm on a side, 0.025 cm thick. We have employed gold pressure
Fig. 3. Montgomery sample configuration.
258
contacts, spring pressure being small enough to avoid distortion of the sample on intercalation. Measurement of the resistances Ra and Rc from top surface and edge measurements, respectively, where the resistances are defined by:
v34
Ra- ~andRc---i12
:
~
FREQUENCY 1 COUNTER FERRITE CORE
i C-axis
,
I15
SAMPLE
permits determination of o~ and o~. These may be defined by the functions Oa = f(Ra' Oc' /1' 12, 13)
(1)
and Oc = g(R~, 0~, ll, 12, 13).
(2)
In principle then, the basal plane conductivity, oa, may be determined self-consistently from these two equations. However, the c-axis conductivity, oc, in eqn. (1) is that representative of a very thin surface layer beneath the top surface contacts. By contrast, the c-axis conductivity defined by eqn. (2) is the bulk averaged value. We suggest that for HOPG, where c-axis conduction is modified by the presence of macroscopic defects, the values of Oc appropriate to the two measurements are not necessarily equal. Self-consistent solution of eqns. (1) and (2) therefore, is not justified. In addition, electric field patterns in the material are disturbed from their theoretical distribution by the presence of defects, dislocations, etc. In consequence, the Montgomery method is inappropriate for precise determination of basal plane conductivities in AsFs--graphite and other acceptor compounds with large e. Nevertheless, we have obtained useful data for AsF5 compounds by this technique [7] which may be summarized as follows: (i) The a-axis conductivity, oa, peaks in the vicinity of stage 2 or 3 with a peak value 2 X 10 5 (~2 a m ) -1 <: o a < 7 X 10 5 (~2 cm) -1. (ii) The anisotropy ratio (~ > 10 6 for stage n <_ 3, is larger than for other material at m room temperature.
(iii) R.f. Technique This technique has m a n y advantages over the two techniques previously discussed. Current is injected inductively in a well-defined manner and the technique is insensitive to the
Fig. 4. Schematic of r.f. technique.
anisotropy in the conductivity, since currents are confined to the basal plane. A schematic of the method is shown in Fig. 4. Eddy currents are induced in the sample when introduced into the r.f. (nominally 100 kHz) magnetic field. The eddy currents correspond to a change in impedance of the resonant circuit and this is reflected in a change of the frequency of oscillation, w. The system relies on a careful calibration of the response (frequency change) as a function of the following sample parameters (i) surface area, s, (ii) thickness, t, (iii) resistivity, p (-1/o). Fits to semi-empirical formulae have been made, on the basis of the calibration, for the two experimental regions of interest. (a) N o n skin-depth regime (5 >> t) [
\p /
\P /
(b) Skin-depth limited region (6 << t) Es 2
AT = p-~ + Fs a + Vts
(4)
where 6 is the classical skin depth, AT is the change in period T (-2x/w) due to the sample, and K1, K2, E, F and G are constants determined from the calibration. Experiments with multilayer composites indicate that the system is rather insensitive to sample exfoliation, which is a c o m m o n feature of intercalation compounds. These experiments also serve to confirm the insensitivity of the technique to the conductivity along the direction of the r.f. magnetic field, i.e., along the c-axis.
259 T h e results p r e s e n t e d in T a b l e 1 show t h a t t h e r.f. m e t h o d gives results in close agreem e n t with c o n v e n t i o n a l t e c h n i q u e s for relatively low a n i s o t r o p y materials (a <_ 104). Use o f t h e r.f. t e c h n i q u e b e c o m e s progressively m o r e i m p o r t a n t as a b e c o m e s larger t h a n 104, and is essential for ~ > 106, i.e., for low stage AsF 5 c o m p o u n d s . F o r these materials we find a peak a-axis c o n d u c t i v i t y occurring at a c o m p o s i t i o n CI~AsFs, o, (6.3 -+ 0.7) × 105 (~2 cm) -1 [ 7 ] . T h e value m a y well be conservative since sample i m p e r f e c t i o n s o f a n y kind c o n t r i b u t e t o a r e d u c t i o n in t h e m e a s u r e d conductivity.
t h e r e b y avoids t h e substantial p r o b l e m s associated with m a k i n g o h m i c c o n t a c t s t o materials in a hostile (highly corrosive) environment.
CONCLUSIONS
REFERENCES
T h e quasi-two-dimensional n a t u r e o f m a n y o f t h e graphite i n t e r c a l a t i o n c o m p o u n d s has demanded a re-examination of traditional t e c h n i q u e s for m e a s u r e m e n t o f electrical cond u c t i v i t y . In a research area w h e r e t h e e x t e n t o f p o t e n t i a l applications d e p e n d s critically o n t h e size o f t h e e n h a n c e d electrical cond u c t i v i t y , a precise and reliable m e t h o d o f m e a s u r e m e n t is called for. U n d e r c o n d i t i o n s o f high a n i s o t r o p y , f o r t h e variety o f reasons cited, we m u s t regard t h e d.c. 4 - p r o b e m e t h o d as generally impractical and likely t o p r o v i d e misleading results. Likewise, t h e M o n t g o m e r y t e c h n i q u e w h e n applied t o these materials, suffers d r a w b a c k s which are hard t o overc o m e . T h e r.f. t e c h n i q u e , b y c o n t r a s t , is simple t o use and is ideally suited t o measurem e n t s o n a n i s o t r o p i c systems. It has t h e addit i o n a l advantage t h a t it is contactless and
1 A. R. Ubbelohde, Proc. R. Soc. London, Ser. A, 327 (1972) 289. 2 C. Zeller, G. M. T. Foley and F. L. Vogel, submitted to J. Mater. Sci. 3 A. R. Ubbelohde, Proc. R. Soc. London, Ser. A, 304 (1968) 25. 4 C. Zeller and J. E. Fischer, unpublished. 5 T. E. Thompson, unpublished. 6 E. R. Falardeau, G. M. T. Foley, C. Zeller and F. L. Vogel, J. Chem. Soc., Chem. Commun., 11 (1977) 389. 7 G.M.T. Foley, C. Zeller, E. R. Falardeau and F. L. Vogel, submitted to Solid State Commun. 8 D. Gu~rard, G. M. T. Foley, M. Zanini and J. E. Fischer, Nuovo Cimento, 38B (1977) 410. 9 J. J. Murray and A. R. Ubbelohde, Proc. R. Soc. London, Set. A, 312 (1969) 371. 10 C. Zeller, unpublished. 11 F. L. Vogel, J. Mater. Sci., 12 (1977) 982. 12 H. C. Montgomery, J. Appl. Phys., 42 (1971) 2971. 13 C. Zeller, A. Denenstein and G. M. T. Foley, submitted to Rev. Sci. Instr.
ACKNOWLEDGEMENTS We t h a n k Dr. A r t h u r M o o r e o f t h e Union Carbide C o r p o r a t i o n for generous provision o f HOPG. We t h a n k also Dr. Daniel Gu~rard for m a n u f a c t u r e o f a CsRb sample. We gratefully a c k n o w l e d g e t h e substantial c o n t r i b u t i o n s o f Dr. Arnold D e n e n s t e i n in design o f the r.f. s y s t e m and in m a n y helpful discussions.
255
@) Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
Measurement of Electrical Conductivity under Conditions of High Anisotropy in Graphite Intercalation Compounds*
C. ZELLER, G. M. T. FOLEY, E. R. F A L A R D E A U and F. L. VOGEL
Moore School of Electrical Engineering and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (U.S.A.)
SUMMARY
Recent measurements of r o o m temperature electrical conductivity in AsFs-graphite intercalation compounds have emphasized the need for a re-evaluation of conventional techniques when applied to quasi-two-dimensional materials. We have thoroughly investigated the validity of the classic 4-point bridge measurement under conditions of high anisotropy and find that for parameters appropriate to some intercalation compounds, such techniques are impractical and lead to serious errors in measured electrical conductivities. In attempting to resolve the difficulties inherent in making measurements of electrical conductivity in these materials we have considered the Montgomery d.c. technique and a novel r.f. method. Measurements on AsFsgraphite by the Montgomery technique appear to give qualitatively correct behavior for resistivity v e r s u s stage and confirm that the magnitude of the anisotropy is larger than that in any previously measured compound. The technique is, however, critically sensitive to crystal defects and this precludes a definitive measurement of a-axis conductivity in these compounds. The r.f. technique which we have developed is, by contrast, insensitive to the degree of anisotropy and is shown to be well suited to the measurement of basal plane conductivities in quasi-two
de mesure conventionnelles appliqu6es ~ des mat6riaux quasi bi
INTRODUCTION RESUME
Des mesures r6centes de conductivit6 6lectriques ~ temp6rature ambiante sur des compos6s d'insertion graphite-AsFs ont indiqu6 clairement la n~cessit6 de reviser les m6thodes *Research supported by NSF DMR75-04954 and MRL/DMR 76-00678.
Relatively little attention has been paid in the past to the significance of the electrical anisotropy as it relates to measurement o f the electrical conductivity in graphite intercalation compounds. Recent results of measurements of the basal plane room temperature electrical conductivity of some of the
256 TABLE 1 a-Axis and c-axis conductivities of HOPG and some graphite intercalation compounds Material
Measurement technique
Bridge method
HOPG Cz2HNO 3 C16AsF 5 C8Rb CsK
r.f. Method
Anisotropy a -=- o a / o c
oa
ac
oa
(~2 cm) -1
(~2 cm) -1
( ~ cm) -1
11.4 [1] 1.96 [3] 0.23 [7] -4.8 x 104 [9]
2.6 × 3.3 x 6.3x 9.1 × --
2.7 x 2.7 × 2.2× 1.0 × 9.5 x
104 105 105 10 5 104
[1] [3] [5] [8] [8]
strong acid-fluoride intercalation compounds of graphite suggest that the choice of measuring technique is crucial. Reference to Table 1, a compilation of a-axis and c-axis conductivities for graphite and several intercalation compounds, reveals a substantial discrepancy between a-axis values for AsFs-graphite from two different types of measurement [5, 6]. The a-axis conductivity from a four point d.c. bridge measurement is almost a factor of three smaller than that derived by an r.f. eddy-current technique. The source of the discrepancy is the very large anisotropy ratio, a (-oa/oc), for AsFsgraphite which exceeds 106 for stages lower than four [7]. This is almost three orders of magnitude larger than the anisotropy ratio for the parent, highly-oriented, pyrolytic graphite [2] (HOPG) and indicates that the compound is quasi-two-dimensional in its electrical properties. The values of Table 1 show that the disparity between bridge measurements and r.f. measurements increases with increasing anisotropy. For HOPG with a ~ 2 000 the agreement between the two methods is rather good, as it is for CaRb [7, 9], where the anisotropy (inferred from that for CsK) [8] is even smaller. However, the acceptor intercalation compounds, in general, show marked increases in ~ over that for HOPG. Moreover, the acceptor compounds have recently become of special interest as possible practical synthetic metals [ 11 ]. It appears to be appropriate therefore, to review the practical and theoretical considerations in making reliable measurements of their room temperature basal plane conductivities.
104 105 105 10 4
[2] [4] [6] [10]
2.3 x 103 [1] 1.4 x 105 [3] 2.7 × 106 [7] -21 [9]
i
-
v
1 c-axis
Fig. 1. Bridge sample configuration.
In that regard we examine three techniques, and results of their application to AsF5graphite. These are the conventional 4-point d.c. bridge technique, the Montgomery method [12] and the r.f. induction technique [13]. Of the three, only the latter is entirely satisfactory.
EXPERIMENTAL TECHNIQUES
(i) The 4-point, d.c. bridge m e t h o d Figure 1 illustrates a typical sample configuration for these measurements. The fundamental premise of the technique is that there exists uniform current density between the voltage contacts. Although this condition is easily met for isotropic samples, in general, the premise can only be satisfied for anisotropic materials for thin samples with current contacts far from the voltage contacts. The necessary sample geometries cannot be achieved with AsFs--graphite where aspect ratios l/t ~- 104 are called for. The problem lies in the distribution of current at a current contact where current is typically injected by means of a gold wire wrapped around the contact and epoxied with a conducting gold cement. The real experi-
257 i
A
Rs
R%
IRWi
Re
RGc
R% ",ANVW,--
Rw i
RB
RGc
RG o
Rw
Re
RGc R% i i i i I
Re
~
R%
Fig. 2. Equivalent circuit for a bridge sample at a current contact.
mental situation is complicated, varies from one experiment to the next, and cannot therefore be modelled exactly. Nevertheless, simple models serve to illustrate the problems involved and enable reasonable conclusions to be drawn with respect to feasibility of 4-point bridge measurements. Figure 2 is a representation of an equivalent circuit for a bridge sample in the region of a current contact. Rw, Rs and RB represent the incremental wire resistance, surface contact resistance and the bulk contact resistance, respectively. RG, and RGc are resistances characterizing conduction along the basal plane and perpendicular to it, respectively. Relative weights of the resistors in the network for AsFs-graphite are: R w ~ RGa ~
Rec
and Rs << R B. The second inequality is motivated by the fact that a two
Further, it is consistent with results observed experimentally for AsFs-graphite. The nonuniform distribution of current is equivalent to an effective sample thickness smaller than the true thickness. This results in the observed underestimation of the basal plane conductivity. Model calculations of a "worst case" situation for AsFs-graphite, in which current is injected into and extracted from the top surface layer of the sample only, indicate resistivities two orders of magnitude higher than those observed experimentally in bridge measurements. While, in practice, therefore, we do not approach the "worst case" configuration, results of a detailed study of bridge measurements under conditions of very high anisotropy (~ >- 105) justify two general conclusions: (i) Uniform current injection at a current contact cannot be achieved in practice. (ii) Once injected non-uniformly, negligible current spreading takes place between the current contacts for samples of any reasonable length. Based on these conclusions, results of electrical conductivity measurements on highly anisotropic materials by the 4-point bridge technique must necessarily be considered unreliable. We therefore completely discount the low (2.2 × 105 (~ cm}-1} a-axis conductivity values for AsFs- graphite indicated in Table 1.
(ii) D.C. Montgomery technique This four-point technique permits determination of the conductivities along the principal directions in an anisotropic solid. For highly anisotropic materials the six-contact configuration of Fig. 3 is necessary. In measurements on AsFs-graphite we have used square plate samples 1 cm on a side, 0.025 cm thick. We have employed gold pressure
Fig. 3. Montgomery sample configuration.
258
contacts, spring pressure being small enough to avoid distortion of the sample on intercalation. Measurement of the resistances Ra and Rc from top surface and edge measurements, respectively, where the resistances are defined by:
v34
Ra- ~andRc---i12
:
~
FREQUENCY 1 COUNTER FERRITE CORE
i C-axis
,
I15
SAMPLE
permits determination of o~ and o~. These may be defined by the functions Oa = f(Ra' Oc' /1' 12, 13)
(1)
and Oc = g(R~, 0~, ll, 12, 13).
(2)
In principle then, the basal plane conductivity, oa, may be determined self-consistently from these two equations. However, the c-axis conductivity, oc, in eqn. (1) is that representative of a very thin surface layer beneath the top surface contacts. By contrast, the c-axis conductivity defined by eqn. (2) is the bulk averaged value. We suggest that for HOPG, where c-axis conduction is modified by the presence of macroscopic defects, the values of Oc appropriate to the two measurements are not necessarily equal. Self-consistent solution of eqns. (1) and (2) therefore, is not justified. In addition, electric field patterns in the material are disturbed from their theoretical distribution by the presence of defects, dislocations, etc. In consequence, the Montgomery method is inappropriate for precise determination of basal plane conductivities in AsFs--graphite and other acceptor compounds with large e. Nevertheless, we have obtained useful data for AsF5 compounds by this technique [7] which may be summarized as follows: (i) The a-axis conductivity, oa, peaks in the vicinity of stage 2 or 3 with a peak value 2 X 10 5 (~2 a m ) -1 <: o a < 7 X 10 5 (~2 cm) -1. (ii) The anisotropy ratio (~ > 10 6 for stage n <_ 3, is larger than for other material at m room temperature.
(iii) R.f. Technique This technique has m a n y advantages over the two techniques previously discussed. Current is injected inductively in a well-defined manner and the technique is insensitive to the
Fig. 4. Schematic of r.f. technique.
anisotropy in the conductivity, since currents are confined to the basal plane. A schematic of the method is shown in Fig. 4. Eddy currents are induced in the sample when introduced into the r.f. (nominally 100 kHz) magnetic field. The eddy currents correspond to a change in impedance of the resonant circuit and this is reflected in a change of the frequency of oscillation, w. The system relies on a careful calibration of the response (frequency change) as a function of the following sample parameters (i) surface area, s, (ii) thickness, t, (iii) resistivity, p (-1/o). Fits to semi-empirical formulae have been made, on the basis of the calibration, for the two experimental regions of interest. (a) N o n skin-depth regime (5 >> t) [
\p /
\P /
(b) Skin-depth limited region (6 << t) Es 2
AT = p-~ + Fs a + Vts
(4)
where 6 is the classical skin depth, AT is the change in period T (-2x/w) due to the sample, and K1, K2, E, F and G are constants determined from the calibration. Experiments with multilayer composites indicate that the system is rather insensitive to sample exfoliation, which is a c o m m o n feature of intercalation compounds. These experiments also serve to confirm the insensitivity of the technique to the conductivity along the direction of the r.f. magnetic field, i.e., along the c-axis.
259 T h e results p r e s e n t e d in T a b l e 1 show t h a t t h e r.f. m e t h o d gives results in close agreem e n t with c o n v e n t i o n a l t e c h n i q u e s for relatively low a n i s o t r o p y materials (a <_ 104). Use o f t h e r.f. t e c h n i q u e b e c o m e s progressively m o r e i m p o r t a n t as a b e c o m e s larger t h a n 104, and is essential for ~ > 106, i.e., for low stage AsF 5 c o m p o u n d s . F o r these materials we find a peak a-axis c o n d u c t i v i t y occurring at a c o m p o s i t i o n CI~AsFs, o, (6.3 -+ 0.7) × 105 (~2 cm) -1 [ 7 ] . T h e value m a y well be conservative since sample i m p e r f e c t i o n s o f a n y kind c o n t r i b u t e t o a r e d u c t i o n in t h e m e a s u r e d conductivity.
t h e r e b y avoids t h e substantial p r o b l e m s associated with m a k i n g o h m i c c o n t a c t s t o materials in a hostile (highly corrosive) environment.
CONCLUSIONS
REFERENCES
T h e quasi-two-dimensional n a t u r e o f m a n y o f t h e graphite i n t e r c a l a t i o n c o m p o u n d s has demanded a re-examination of traditional t e c h n i q u e s for m e a s u r e m e n t o f electrical cond u c t i v i t y . In a research area w h e r e t h e e x t e n t o f p o t e n t i a l applications d e p e n d s critically o n t h e size o f t h e e n h a n c e d electrical cond u c t i v i t y , a precise and reliable m e t h o d o f m e a s u r e m e n t is called for. U n d e r c o n d i t i o n s o f high a n i s o t r o p y , f o r t h e variety o f reasons cited, we m u s t regard t h e d.c. 4 - p r o b e m e t h o d as generally impractical and likely t o p r o v i d e misleading results. Likewise, t h e M o n t g o m e r y t e c h n i q u e w h e n applied t o these materials, suffers d r a w b a c k s which are hard t o overc o m e . T h e r.f. t e c h n i q u e , b y c o n t r a s t , is simple t o use and is ideally suited t o measurem e n t s o n a n i s o t r o p i c systems. It has t h e addit i o n a l advantage t h a t it is contactless and
1 A. R. Ubbelohde, Proc. R. Soc. London, Ser. A, 327 (1972) 289. 2 C. Zeller, G. M. T. Foley and F. L. Vogel, submitted to J. Mater. Sci. 3 A. R. Ubbelohde, Proc. R. Soc. London, Ser. A, 304 (1968) 25. 4 C. Zeller and J. E. Fischer, unpublished. 5 T. E. Thompson, unpublished. 6 E. R. Falardeau, G. M. T. Foley, C. Zeller and F. L. Vogel, J. Chem. Soc., Chem. Commun., 11 (1977) 389. 7 G.M.T. Foley, C. Zeller, E. R. Falardeau and F. L. Vogel, submitted to Solid State Commun. 8 D. Gu~rard, G. M. T. Foley, M. Zanini and J. E. Fischer, Nuovo Cimento, 38B (1977) 410. 9 J. J. Murray and A. R. Ubbelohde, Proc. R. Soc. London, Set. A, 312 (1969) 371. 10 C. Zeller, unpublished. 11 F. L. Vogel, J. Mater. Sci., 12 (1977) 982. 12 H. C. Montgomery, J. Appl. Phys., 42 (1971) 2971. 13 C. Zeller, A. Denenstein and G. M. T. Foley, submitted to Rev. Sci. Instr.
ACKNOWLEDGEMENTS We t h a n k Dr. A r t h u r M o o r e o f t h e Union Carbide C o r p o r a t i o n for generous provision o f HOPG. We t h a n k also Dr. Daniel Gu~rard for m a n u f a c t u r e o f a CsRb sample. We gratefully a c k n o w l e d g e t h e substantial c o n t r i b u t i o n s o f Dr. Arnold D e n e n s t e i n in design o f the r.f. s y s t e m and in m a n y helpful discussions.